%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI693_1 : TPTP v8.1.2. Released v6.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n012.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 17:48:50 EDT 2023 % Result : Theorem 3.11s 1.18s % Output : Proof 3.64s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : ARI693_1 : TPTP v8.1.2. Released v6.3.0. % 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n012.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Tue Aug 29 17:42:24 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.17/1.05 Prover 0: Preprocessing ... % 2.17/1.05 Prover 6: Preprocessing ... % 2.17/1.05 Prover 2: Preprocessing ... % 2.17/1.05 Prover 1: Preprocessing ... % 2.17/1.05 Prover 3: Preprocessing ... % 2.17/1.05 Prover 5: Preprocessing ... % 2.17/1.05 Prover 4: Preprocessing ... % 2.67/1.11 Prover 1: Constructing countermodel ... % 2.67/1.11 Prover 6: Constructing countermodel ... % 2.67/1.11 Prover 5: Constructing countermodel ... % 2.67/1.11 Prover 2: Constructing countermodel ... % 2.67/1.11 Prover 3: Constructing countermodel ... % 2.67/1.11 Prover 4: Constructing countermodel ... % 2.67/1.11 Prover 0: Constructing countermodel ... % 3.11/1.17 Prover 3: proved (539ms) % 3.11/1.17 Prover 5: proved (536ms) % 3.11/1.17 % 3.11/1.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.11/1.18 % 3.11/1.18 % 3.11/1.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.11/1.18 % 3.11/1.18 Prover 0: proved (543ms) % 3.11/1.18 % 3.11/1.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.11/1.18 % 3.11/1.18 Prover 6: stopped % 3.11/1.18 Prover 2: stopped % 3.11/1.18 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.11/1.18 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.11/1.18 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.11/1.18 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.11/1.18 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.11/1.19 Prover 11: Preprocessing ... % 3.11/1.20 Prover 8: Preprocessing ... % 3.11/1.20 Prover 1: Found proof (size 31) % 3.11/1.20 Prover 1: proved (569ms) % 3.11/1.20 Prover 10: Preprocessing ... % 3.11/1.20 Prover 7: Preprocessing ... % 3.11/1.21 Prover 11: Constructing countermodel ... % 3.11/1.21 Prover 4: Found proof (size 30) % 3.11/1.21 Prover 4: proved (575ms) % 3.11/1.21 Prover 11: stopped % 3.11/1.21 Prover 10: Constructing countermodel ... % 3.11/1.21 Prover 10: stopped % 3.11/1.21 Prover 13: Preprocessing ... % 3.11/1.21 Prover 8: Constructing countermodel ... % 3.11/1.22 Prover 7: Constructing countermodel ... % 3.11/1.22 Prover 8: stopped % 3.11/1.22 Prover 7: stopped % 3.11/1.23 Prover 13: Constructing countermodel ... % 3.11/1.23 Prover 13: stopped % 3.11/1.23 % 3.11/1.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.11/1.23 % 3.11/1.24 % SZS output start Proof for theBenchmark % 3.11/1.24 Assumptions after simplification: % 3.11/1.24 --------------------------------- % 3.11/1.24 % 3.11/1.24 (conj) % 3.11/1.25 ? [v0: int] : ( ~ (v0 = 0) & $lesseq(v0, 169) & $lesseq(-169, v0) & ? [v1: % 3.11/1.25 int] : $difference($sum($product(170, v1), v0), z) = -54 & ( ~ % 3.11/1.25 ($lesseq(v0, -1)) | ~ ($lesseq(-116, z))) & ( ~ ($lesseq(1, v0)) | ~ % 3.11/1.25 ($lesseq(z, -116)))) % 3.11/1.25 % 3.11/1.25 (eq1) % 3.11/1.25 $sum($product(5, a), $product(3, x)) = 1 % 3.11/1.25 % 3.11/1.25 (eq2) % 3.11/1.25 $difference($product(7, z), $product(17, x)) = 4 % 3.11/1.25 % 3.11/1.25 (eq3) % 3.11/1.25 $sum($product(2, y), $product(7, x)) = -34 % 3.11/1.25 % 3.11/1.25 Those formulas are unsatisfiable: % 3.11/1.25 --------------------------------- % 3.11/1.25 % 3.11/1.25 Begin of proof % 3.11/1.25 | % 3.11/1.25 | DELTA: instantiating (conj) with fresh symbol all_3_0 gives: % 3.11/1.25 | (1) ~ (all_3_0 = 0) & $lesseq(all_3_0, 169) & $lesseq(-169, all_3_0) & ? % 3.11/1.25 | [v0: int] : $difference($sum($product(170, v0), all_3_0), z) = -54 & ( % 3.11/1.25 | ~ ($lesseq(all_3_0, -1)) | ~ ($lesseq(-116, z))) & ( ~ ($lesseq(1, % 3.11/1.25 | all_3_0)) | ~ ($lesseq(z, -116))) % 3.11/1.25 | % 3.11/1.25 | ALPHA: (1) implies: % 3.11/1.25 | (2) ~ (all_3_0 = 0) % 3.11/1.25 | (3) $lesseq(-169, all_3_0) % 3.11/1.25 | (4) $lesseq(all_3_0, 169) % 3.11/1.25 | (5) ? [v0: int] : $difference($sum($product(170, v0), all_3_0), z) = -54 % 3.11/1.25 | % 3.11/1.25 | DELTA: instantiating (5) with fresh symbol all_5_0 gives: % 3.11/1.26 | (6) $difference($sum($product(170, all_5_0), all_3_0), z) = -54 % 3.11/1.26 | % 3.11/1.26 | COL_REDUCE: introducing fresh symbol sc_7_0_0 defined by: % 3.11/1.26 | (7) all_5_0 = sc_7_0_0 % 3.11/1.26 | % 3.11/1.26 | COMBINE_EQS: (6), (7) imply: % 3.11/1.26 | (8) $sum($difference(all_3_0, z), $product(170, sc_7_0_0)) = -54 % 3.11/1.26 | % 3.11/1.26 | COL_REDUCE: introducing fresh symbol sc_7_0_1 defined by: % 3.11/1.26 | (9) $difference($sum(y, $product(3, x)), sc_7_0_1) = -17 % 3.11/1.26 | % 3.11/1.26 | COMBINE_EQS: (9), (eq3) imply: % 3.11/1.26 | (10) $sum(x, $product(2, sc_7_0_1)) = 0 % 3.11/1.26 | % 3.11/1.26 | COMBINE_EQS: (10), (eq1) imply: % 3.11/1.26 | (11) $difference($product(5, a), $product(6, sc_7_0_1)) = 1 % 3.11/1.26 | % 3.11/1.26 | COMBINE_EQS: (10), (eq2) imply: % 3.11/1.26 | (12) $sum($product(7, z), $product(34, sc_7_0_1)) = 4 % 3.11/1.26 | % 3.11/1.26 | COL_REDUCE: introducing fresh symbol sc_7_0_2 defined by: % 3.11/1.26 | (13) $difference($sum(z, $product(5, sc_7_0_1)), sc_7_0_2) = 1 % 3.11/1.26 | % 3.11/1.26 | COMBINE_EQS: (12), (13) imply: % 3.11/1.26 | (14) $difference(sc_7_0_1, $product(7, sc_7_0_2)) = 3 % 3.11/1.26 | % 3.11/1.26 | SIMP: (14) implies: % 3.11/1.26 | (15) $difference(sc_7_0_1, $product(7, sc_7_0_2)) = 3 % 3.11/1.26 | % 3.11/1.26 | COMBINE_EQS: (11), (15) imply: % 3.11/1.26 | (16) $difference($product(5, a), $product(42, sc_7_0_2)) = 19 % 3.11/1.26 | % 3.11/1.26 | COMBINE_EQS: (13), (15) imply: % 3.11/1.26 | (17) $sum(z, $product(34, sc_7_0_2)) = -14 % 3.11/1.26 | % 3.11/1.26 | COMBINE_EQS: (8), (17) imply: % 3.11/1.26 | (18) $sum($sum(all_3_0, $product(170, sc_7_0_0)), $product(34, sc_7_0_2)) = % 3.11/1.26 | -68 % 3.11/1.26 | % 3.11/1.26 | COL_REDUCE: introducing fresh symbol sc_7_0_3 defined by: % 3.11/1.26 | (19) $difference($difference(a, $product(8, sc_7_0_2)), sc_7_0_3) = 4 % 3.11/1.26 | % 3.11/1.26 | COMBINE_EQS: (16), (19) imply: % 3.11/1.26 | (20) $difference($product(2, sc_7_0_2), $product(5, sc_7_0_3)) = 1 % 3.11/1.26 | % 3.11/1.26 | SIMP: (20) implies: % 3.11/1.26 | (21) $difference($product(2, sc_7_0_2), $product(5, sc_7_0_3)) = 1 % 3.11/1.26 | % 3.11/1.26 | COMBINE_EQS: (18), (21) imply: % 3.11/1.26 | (22) $sum($sum(all_3_0, $product(170, sc_7_0_0)), $product(85, sc_7_0_3)) = % 3.11/1.26 | -85 % 3.11/1.26 | % 3.11/1.26 | COL_REDUCE: introducing fresh symbol sc_7_0_4 defined by: % 3.11/1.26 | (23) $difference($difference(sc_7_0_2, $product(3, sc_7_0_3)), sc_7_0_4) = % 3.64/1.26 | 1 % 3.64/1.26 | % 3.64/1.26 | COMBINE_EQS: (21), (23) imply: % 3.64/1.26 | (24) $sum(sc_7_0_3, $product(2, sc_7_0_4)) = -1 % 3.64/1.26 | % 3.64/1.26 | COMBINE_EQS: (22), (24) imply: % 3.64/1.27 | (25) $sum(all_3_0, $product(170, sc_7_0_0)) = $product(170, sc_7_0_4) % 3.64/1.27 | % 3.64/1.27 | REDUCE: (4), (25) imply: % 3.64/1.27 | (26) $lesseq(sc_7_0_4, sc_7_0_0) % 3.64/1.27 | % 3.64/1.27 | SIMP: (26) implies: % 3.64/1.27 | (27) $lesseq(sc_7_0_4, sc_7_0_0) % 3.64/1.27 | % 3.64/1.27 | REDUCE: (3), (25) imply: % 3.64/1.27 | (28) $lesseq(sc_7_0_0, sc_7_0_4) % 3.64/1.27 | % 3.64/1.27 | SIMP: (28) implies: % 3.64/1.27 | (29) $lesseq(sc_7_0_0, sc_7_0_4) % 3.64/1.27 | % 3.64/1.27 | REDUCE: (2), (25) imply: % 3.64/1.27 | (30) ~ (sc_7_0_0 = sc_7_0_4) % 3.64/1.27 | % 3.64/1.27 | SIMP: (30) implies: % 3.64/1.27 | (31) ~ (sc_7_0_0 = sc_7_0_4) % 3.64/1.27 | % 3.64/1.27 | STRENGTHEN: (27), (31) imply: % 3.64/1.27 | (32) $lesseq(1, $difference(sc_7_0_0, sc_7_0_4)) % 3.64/1.27 | % 3.64/1.27 | COMBINE_INEQS: (29), (32) imply: % 3.64/1.27 | (33) $false % 3.64/1.27 | % 3.64/1.27 | CLOSE: (33) is inconsistent. % 3.64/1.27 | % 3.64/1.27 End of proof % 3.64/1.27 % SZS output end Proof for theBenchmark % 3.64/1.27 % 3.64/1.27 657ms %------------------------------------------------------------------------------